Some endpoint estimates for bilinear Coifman-Meyer multipliers

Abstract

In this paper we establish mapping properties of bilinear Coifman-Meyer multipliers acting on the product spaces $H^1({\mathbb{R}}^n)\times \mathrm{bmo}({\mathbb{R}}^n)$ and $L^p({\mathbb{R}}^n)\times \mathrm{bmo}({\mathbb{R}}^n)$, with $1<p<\infty$. As application of these results, we obtain some related Kato-Ponce-type inequalities involving the endpoint space $\mathrm{bmo}({\mathbb{R}}^n)$, and we also study the pointwise product of a function in $\mathrm{bmo}({\mathbb{R}}^n)$ with functions in $H^1({\mathbb{R}}^n)$, $h^1({\mathbb{R}}^n)$ and $L^p({\mathbb{R}}^n)$, with $1<p<\infty$.